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Ural Mathematical Journal
Scopus
ISSN 2414-3952 · Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics · 264 articles in the index
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Journal Article
APPROXIMATION OF FUNCTIONS USING EXTENDED CHEBYSHEV WAVELETS AND ITS APPLICATION IN SOLVING INTEGRAL EQUATIONS
TThis paper presents a novel method in wavelet analysis for approximating solution functions of Fredholm integral equations. The proposed approach uses partial sums derived from this expansion on the interval \([0,\gamma)\), where \(\gamma>0\), resulting in accurate approximations of the solution…
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Journal Article
APPROXIMATIONS OF THE SET OF TRAJECTORIES, ATTAINABLE SETS AND INTEGRAL FUNNEL OF NONLINEAR CONTROL SYSTEMS WITH MIXED CONSTRAINTS ON THE CONTROL FUNCTIONS
In this paper, approximations of the set of trajectories, attainable sets and integral funnel of a control system described by a nonlinear ordinary differential equation with mixed constraints on the control functions are discussed. The set of admissible control functions is replaced by a set…
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Journal Article
EXISTENCE OF SOLUTIONS OF FRACTIONAL EQUATION WITH NEW BOUNDARY CONDITIONS
In this paper, we investigate a nonlinear fractional integro-differential equation involving Caputo fractional derivatives together with nonlocal boundary conditions. In contrast to some existing works, the problem is considered with homogeneous initial conditions. By applying Krasnoselskii's…
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Journal Article
A PROCEDURE FOR DERIVING ODD-GRACEFUL CHROMATIC NUMBERS OF GRAPHS
Let \(G:=(V,E)\) be an undirected finite simple graph with vertex set \(V\) and edge set \(E\). A function \(c:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\), such that \(c(u)\neq c(v)\) for every edge \(uv\in E(G)\), is called a (proper) vertex \(k\)-colouring of \(G\). If…
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Journal Article
EXISTENCE AND ULAM–HYERS STABILITY OF SOLUTIONS FOR SOME BACKWARD IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES
This paper investigates the existence and generalized Ulam–Hyers stability of solutions for a class of nonlinear backward impulsive fractional differential equations in Banach spaces with both local and nonlocal conditions. By reformulating the problem as an equivalent integral equation, we apply…
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Journal Article
CHEBYSHEV POLYNOMIALS ON REGULAR POLYGONS IN THE COMPLEX PLANE
The Chebyshev problem is studied for a regular \(m\)-gon \(G_m\), \(m\geq 3\), in the complex plane \(\mathbb{C}\). Let \(\mathscr{P}_n^1\) be the set of algebraic polynomials of a given degree \(n\) with unit leading coefficient. The problem is to find the smallest value \(\tau_n(G_m)\) of the…
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Journal Article
NEARLY COMPLETE STRONG SEMILATTICE OF LEFT GROUPS
This study provides significant insights into the structure and behavior of a strong semilattice of left groups, establishing a solid foundation for future research in this domain. The work commences by presenting significant findings about endomorphisms and inner automorphisms of these semigroups…
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Journal Article
SUBSPACE IDENTIFICATION METHOD FOR STOCHASTIC LINEAR CONTROL SYSTEMS
Subspace identification is studied for stochastic linear control systems in state-space form. PO-MOESP (Past Outputs Multivariable Output-Error State sPace) algorithm is described, implemented and compared with other subspace identification methods and classical parametric methods. The presentation…
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Journal Article
LOCKS AND FORBIDDEN CONFIGURATIONS IN 4-GRACEFUL TREES
Let \(f\) be a proper coloring of the vertices of a simple graph \(G\) into colors from the set of colors \(\{1, 2, \dots, k\}\). A coloring \(f\) on the set of edges of a graph \(G\) induces a function \(f'(e) = \vert{}f(u) - f(v)\vert{}\), where \(e = uv\) is an arbitrary edge of the graph \(G\)…
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Journal Article
BOUNDEDNESS OF THE DISCRETE HILBERT TRANSFORM ON DISCRETE WEIGHTED MORREY SPACES
The Hilbert transform is a multiplier operator widely used in the theory of Fourier transforms. It was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in many areas of science and technology and plays an important role in digital signal…
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Journal Article
STECHKIN PROBLEM FOR A DIFFERENTIATION OPERATOR WITH ASYMMETRIC CONSTRAINTS
The Landau–Kolmogorov inequality estimates the norm of an intermediate derivative by the product of the norms of the function and its highest-order derivative. The corresponding Stechkin problem concerns the best approximation of the differentiation operator by bounded linear operators. In this…
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Journal Article
MITTAG-LEFFLER STABILITY OF AN ASYMPTOTICALLY \(\omega\)-PERIODIC SOLUTION TO A DELAYED CELLULAR NEURAL SYSTEM
By using fixed-point methods and the properties of \(S\nu\)-asymptotically \(\omega\)-periodic solutions, we establish the existence, uniqueness, exponential stability, and Mittag-Leffler stability of \(S\nu\)-asymptotically \(\omega\)-periodic solutions for several models of recurrent neural…
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Journal Article
TWO METHODS OF DESCRIBING 2-LOCAL DERIVATIONS AND AUTOMORPHISMS
In the present paper, we investigate 2-local linear operators on vector spaces. Sufficient conditions are obtained for the linearity of a 2-local linear operator on a finite-dimensional vector space. To do this, families of matrices of a certain type are selected and it is proved that every 2-local…
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Journal Article
ATTRACTION SETS IN ATTAINABILITY PROBLEMS WITH ASYMPTOTIC-TYPE CONSTRAINTS
In control theory, the problem of constructing and investigating attainability domains is very important. However, under perturbations of constraints, this problem lacks stability. It is useful to single out the case when the constraints are relaxed. In this case, greater opportunities arise in…
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Journal Article
ASYMPTOTIC BEHAVIOR FOR THE LOTKA–VOLTERRA EQUATION WITH DISPLACEMENTS AND DIFFUSION
In this paper, we consider the Lotka–Volterra equation with displacements and diffusion, that is transport-diffusion system describing the evolution of prey and predator populations with their displacements and their diffusion, in a periodic domain in \(\mathbb{R}\). It is shown that the solution…
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Journal Article
ON AN INITIAL BOUNDARY–VALUE PROBLEM FOR A DEGENERATE EQUATION OF HIGH EVEN ORDER
In this paper, we formulate and study an initial boundary-value problem of the type of the third boundary condition for a degenerate partial differential equation of high even order in a rectangle. Using the Fouriers method, based on separation of variables, a spectral problem for an ordinary…
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Journal Article
TOPOLOGIES ON THE FUNCTION SPACE \(Y^X\) WITH VALUES IN A TOPOLOGICAL GROUP
Let \(Y^X\) denote the set of all functions from \(X\) to \(Y\). When \(Y\) is a topological space, various topologies can be defined on \(Y^X\). In this paper, we study these topologies within the framework of function spaces. To characterize different topologies and their properties, we employ…
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Journal Article
A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS
Perfect Italian Domination is a type of vertex domination which can also be viewed as a graph labelling problem. The vertices of a graph \(G\) are labelled by 0, 1 or 2 in such a way that a vertex labelled 0 should have a neighbourhood with exactly two vertices in it labelled 1 each or with exactly…
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Journal Article
A REMARK AND AN IMPROVED VERSION ON RECENT RESULTS CONCERNING RATIONAL FUNCTIONS
This paper extends as a lemma an auxiliary result obtained by Singh and Chanam. Using it, we prove a refinement of the Turán-type inequality for rational functions obtained recently by Akhter et al. Next, using examples, we discuss the result of Mir et al.
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Journal Article
THE IMPACT OF TOXICANTS IN THE MARINE THREE ECOLOGICAL FOOD-CHAIN ENVIRONMENT: A MATHEMATICAL APPROACH
To explore the impact of toxicants on a marine ecological food chain system consisting of three species, this work develops and analyzes a non-linear mathematical model. The model consists of five state variables: phytoplankton, zooplankton, fish, environmental toxicant, and organismal toxicant. We…